Can files survive partition table and file system recreation? By `GNU parted` I created new DOS partition table, one partition and by `mkfs.ext2` ext2 file system on that partition. I copied some files to that partition. After that I again created new DOS partition table, one partition and ext2 file system on the same HDD. When I mounted this partition some files still was there. Is it possible that files survive partition and file system recreation?

Yes it's possible if you delete and re-create your partition from the exact same sector. The system does not a "full format" when you create your file system. By the way, you can do the same to extend a partition. Delete and recreate it starting from the same sector and ending on a further one